- The random variable \(X\) is normally distributed with unknown mean \(\mu\) and known variance \(\sigma ^ { 2 }\)
A random sample of 25 observations of \(X\) produced a \(95 \%\) confidence interval for \(\mu\) of (26.624, 28.976)
- Find the mean of the sample.
- Show that the standard deviation is 3
The \(a\) \% confidence interval using the 25 observations has a width of 2.1
- Calculate the value of \(a\)
- Find the smallest sample size, of observations from \(X\), that would be required to obtain a 95\% confidence interval of width at most 1.5